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Resonance, and Now Magnifiers Discussion
Edited/Updated: October 23, 2004
This page is a mess, I believe 'Alterations worth doing?' is the antecedent to the 'Resonance, and Now Mag's' discussion. I'll sort it out soon. J. C.
Subject: Re: Alterations worth doing? Date: Wed, 21 Jul 2004 17:49:47 -0600
Original poster: Ed Phillips
Tom, You can always add an "off-axis" auxiliary coil in series with your
primary. Contrary to intuition, adding additional inductance not coupled
to the secondary does not significantly reduce the overall "efficiency" of your
coil.
--Steve Y"
Correct, but adding additional inductance requires closer spacing of the
secondary and the "real primary". I've used a roller coil out of an old
transmitter, with a pulley on the shaft and nylon cord for remote control.
The "fine tuning" showed up only for low power inputs where streamer
formation was pretty sparse. As the power goes up and the streamers form
tighter coupling is needed and the resonant frequency lowered. Ed.
Date: Mon, 19 Jul 2004 21:04:17 -0600. Resent-Date: Mon, 19 Jul 2004 21:08:39 -0600
Original poster: Paul Nicholson
>From another thread:
> Using a large top load capacitance ... helps force the best resonant point
near the 1/4 lambda >point.
This doesn't make any sense, although something along these lines is often heard
from experienced coilers. It sounds as if we're supposed to choose the
topload C so as to make the resonance a 1/4 wave. Larges toploads are
certainly good, but the justification in terms of tuning to some quarter-wave
point is faulty.
It's a 1/4 wave resonance regardless of how much extra C, if any, is added. We
can list some of the changes that occur as top C is added:-
* All the mode frequencies move down. The fundamental (1/4 wave) moves
down more than the overtones.
The remaining points all refer to the 1/4 wave mode...
* The coil current becomes more uniform.
* As a consequence, the effective inductance becomes closer to the low-frequency
inductance, Ldc. For coils with h/d more than about 1.5, this means
the effective inductance increases.
* Because Les moves closer to Ldc, the coil's effective capacitance becomes
closer to the Medhurst value, so the calculation Fres = 1/(2*pi*sqrt(Ldc *(C_med
+ C_top)) gives a more accurate prediction of Fres as top C is increased.
The benefits to the coiler of the heavily toploaded coil are, possibly:-
* Now the fundamental is much lower than the overtones, so we may find less of
the bang energy is going into these higher modes.
* The large top C makes plenty of charge and energy available for streamer
formation.
* The frequency is more accurately predicted by a simple calculation involving
C_medhurst.
* The topload controls the E-field gradient around the coil, protecting the top
turns from breakout, but also shapes the wider field to that breakout tends to
develop horizontally outwards from the toroid, as opposed to taking the shortest
distance (vertically downwards) to earth, or looping back into the coil itself.
The secondary resonance itself offers no meaningful target by way of a specific
value for top loading. It will happily display quarter-wave behaviour with
any top C. I think the choice of a large topload is made purely to
obtain a favourable, or even optimum, coupling between the secondary and the
discharge/streamer load.
Perhaps I can throw in a few words about magnifiers? For these comments
I'll treat the joint secondary-tertiary as a single resonator.
I've described how end-loading pulls down the fundamental much more than the
higher modes. With the magnifier, we exploit the next higher mode of the
resonator - the 3/4 wave, as well as the fundamental. The idea is to tune
the 3/4 wave mode so that it will reach the voltage peak of its alternating
cycle at the same instant as does the fundamental. This will increase the output
voltage beyond that of a similar coil whose 3/4 wave mode is just left to some
random tuning.
To tune the 3/4 mode, we must pull its frequency down from the unloaded value so
that it has the correct frequency relationship to the fundamental.
Applying end loading pulls both modes down and gets us part of the way.
But obviously we need to control the 3/4 wave frequency independently of the 1/4
wave. We do this by applying more external capacitance, but this time
attaching it near the other voltage maxima of the 3/4 wave mode - say about
1/3rd the way up the resonator.
This 'middle' capacitance affects the 3/4 wave mode more than the 1/4 wave mode,
so we now have the means of tuning each mode with some independence of the
other. This tends to be done by splitting the coil at the appropriate
point and maintaining the connection with a piece of wire (the 'transmission
line' of magnifier terminology). The resonator now finds extra capacitive
loading near its 3/4 wave voltage maxima: the top end-effect C of the secondary,
plus the transmission line C, plus the lower end-effect C of the tertiary.
If done correctly, the 3/4 wave mode is now timed to reach a voltage peak
simultaneously with the fundamental after a certain (design choice) number of RF
cycles have elapsed.
Why bother going to all this trouble? Well the 3/4 wave mode is excited
anyway, to some extent, whether we like it or not. So rather than waste
that energy, we might as well try to use it. The extent to which
higher modes are excited in any coil depends on how the primary induction is
distributed along the coil. If we want to achieve high coupling (for
what-ever reason) we cannot do so by spreading the primary along the secondary,
for reasons of voltage breakdown. So we have to apply strong coupling to
just a short region of the secondary at its cold end. It's this highly
end-concentrated coupling which tends to put a greater proportion of the bang
energy into the higher resonances of the secondary. Therefore it's a
natural evolution of the TC to try to tame and exploit these.[*]
I've described all this to show how a bit of 'distributed' theory can be applied
to understand the motivation for constructing magnifiers. (I must point out that
when coilers think about magnifiers, they don't usually think about them in the
kind of terms that I've used above). Antonio has thoroughly documented
this tuning of multiple resonance networks using the lumped model,
http://www.coe.ufrj.br/~acmq/tesla/magnifier.html
(There are of course 3 modes in operation in the magnifier, not just the two I
mentioned above. The primary coil adds adds another relevant degree of
freedom and when this is coupled to the secondary we find an additional 1/2 wave
mode at work along the secondary-tertiary. This too is tuned to
reach a top-volts peak simultaneously with the other two.) [+]
You can see some modelled results for the mode spectrum of Thor, in the last two
graphs in
http://www.abelian.demon.co.uk/tssp/tmod.html
This isn't a magnifier, just a heavily toploaded TC, but it shows the predicted
levels and current distributions of each of the resonances.
Coiler's don't tend to take much notice of the higher order resonances of either
primary or secondary. Many perhaps don't even realise they are there -
mistaking the behaviour of the LC model for that of the real coil. Some
coilers will admit that the secondary has lots of resonances, but will insist
that the primary has only one, thinking perhaps that because it is more 'lumped'
it is working in some basically different way.
I should think most of the time this lack of awareness isn't any problem, after
all the coils work. But I think it's useful to build up a mental picture
of the distributed resonance, if only for the coiler's satisfaction of having a
deeper understanding of the coil's behaviour.
And there's always the hypothesis that some of this HF activity may contribute
to the racing arc phenomena. If for example, one of the primary resonances
happens to be similar in frequency to one of the secondary resonances. Say
the first primary overtone collided with, say, the 5th overtone of the
secondary, there's nothing to prevent the two coils transferring energy back and
forth at these high frequencies.
Admittedly the various overtone amplitudes are small compared with fundamental.
But set against this is the fact that the peak-trough distance of the overtone
standing waves spans fewer turns along the coil than does the fundamental -
fewer in inverse proportion to the number of quarter-waves.
Plus they sit atop the pedestal of the large 1/4 wave voltage, so at the very
least they will eat into the coil's breakdown 'headroom'.
Racing arcs tend to be cured by small adjustments to topload height or coupling,
eg raising the secondary or lowering the primary. When we model
these kind of changes, we don't see any great change in the voltage gradients
reached. Nor do models show any real gradient problems under out of tune
conditions. One wonders then why the real coils seem to show such
sensitivity to coupling and topload height with respect to racing arcs.
One thing our models *don't* account for is the effect of primary overtones.
It may be conceivable that the small adjustments mentioned are having the side
effect of shifting the mode spectra of one or both coils with the unwitting
consequence of removing a nasty collision of HF resonances.
Finally, returning to the issue of large toploads. A point not mentioned
earlier is that the higher overtones of the secondary are available at the top
of the coil at a rather low impedance, thanks largely to the top-C. It
might be the case that this low impedance HF energy contributes to streamer
heating during breakout, helping to keep things cooking nicely in between the
rather lower frequency ebbs and flows of the quarter-wave current.
Magnifiers, for example, are likely to have higher overtone amplitudes than
regular TCs, and so might be predicted to give brighter streamers for a given
streamer length.
Anyway, there must be some food for thought and experiment in there somewhere.
[*] This phenomena of 'concentrated induction near at the end of the coil'
leading to 'greater proportion of energy in the higher overtones' is a fairly
general phenomena. I like to demonstrate it with an effect familiar to
guitar players. As the string is plucked closer to the bridge, the tone becomes
brighter as the overtones (almost harmonics in this case) take up a greater
proportion in the mix of string vibrations that give the guitar its tone.
The guitarist is changing the shape of the initial (triangular) displacement of
the string. The essential physics is that the mix of mode amplitudes (and
phases) must be such that the superposition of all the modes at t=0 along the
string (or coil) equals the initial displacement distribution. This is a
Fourier-like synthesis in the spatial domain, with the normal modes of the
string as basis functions.
[+] As Antonio shows, the idea extends to include many overtones. As more
and more overtones are tuned into coherence at the voltage peak, the TC
operation becomes more pulse-like compared with the leisurely sinusoidal energy
transfer of the normal TC. Paul Nicholson.
Date: Mon, 19 Jul 2004 21:26:12 -0600
Original poster: Terry Fritz
Hi,
At 05:26 PM 7/19/2004, you wrote:
> >From another thread:
> > Using a large top load capacitance.Helps force the best resonant point near the 1/4 lamda point.
>
>This doesn't make any sense, although something along these lines is often heard from
>experienced coilers. It sounds as if we're supposed to choose the topload C so as to make the
>resonance a 1/4 wave. Larges toploads are certainly good, but the justification in terms of tuning to some quarter-wave point is faulty.
>
>It's a 1/4 wave resonance regardless of how much extra C, if any, is added. We can list some of the
>changes that occur as top C is added:-
All the 1/4 wave stuff comes from folks trying to use 1/4 wave antenna models to
predict Tesla coil parameters. It sort of works a little... But
Tesla coils are not at all 1/4 wave antennas... Lumped LC models with
Medhurst and a little fudging work very well for the needs of tuning a coil.
Tesla coils are not true LC lumped networks either, but the models there work
vastly better for day-to-day needs. Tesla coils with arcs have pretty
substantial power dissipative top loading too...
>* All the mode frequencies move down. The fundamental (1/4 wave) moves
down more than the overtones.
>
>The remaining points all refer to the 1/4 wave mode...
>
>* The coil current becomes more uniform.
>* As a consequence, the effective inductance becomes closer
>to the low-frequency inductance, Ldc. For coils with h/d
>more than about 1.5, this means the effective inductance increases.
>* Because Les moves closer to Ldc, the coil's effective
>capacitance becomes closer to the Medhurst value, so the
>calculation Fres = 1/(2*pi*sqrt(Ldc *(C_med + C_top)) gives
>a more accurate prediction of Fres as top C is increased.
>
>The benefits to the coiler of the heavily toploaded coil are, possibly:-
>
>* Now the fundamental is much lower than the overtones, so
>we may find less of the bang energy is going into these higher modes.
>* The large top C makes plenty of charge and energy available for streamer formation.
Yes!! ;-))
>* The frequency is more accurately predicted by a simple calculation involving C_medhurst.
The large C dominates, and makes the simple models work better.
>* The topload controls the E-field gradient around the coil,
>protecting the top turns from breakout, but also shapes the
>wider field to that breakout tends to develop horizontally
>outwards from the toroid, as opposed to taking the shortest
>distance (vertically downwards) to earth, or looping back into the coil itself.
Yes!!
>The secondary resonance itself offers no meaningful target by
>way of a specific value for top loading. It will happily
>display quarter-wave behaviour with any top C. I think the
>choice of a large topload is made purely to obtain a favourable,
>or even optimum, coupling between the secondary and the discharge/streamer load.
It appears that any top C, regardless of secondary wire length, works fine if
tuned.
>Perhaps I can throw in a few words about magnifiers?
>For these comments I'll treat the joint secondary-tertiary as a single resonator.
>
>I've described how end-loading pulls down the fundamental much
>more than the higher modes. With the magnifier, we exploit
>the next higher mode of the resonator - the 3/4 wave, as well
>as the fundamental. The idea is to tune the 3/4 wave mode so
>that it will reach the voltage peak of its alternating cycle
>at the same instant as does the fundamental. This will increase
>the output voltage beyond that of a similar coil whose 3/4 wave
>mode is just left to some random tuning.
>
>To tune the 3/4 mode, we must pull its frequency down from
>the unloaded value so that it has the correct frequency
>relationship to the fundamental. Applying end loading pulls
>both modes down and gets us part of the way. But obviously
>we need to control the 3/4 wave frequency independantly of
>the 1/4 wave. We do this by applying more external capacitance,
>but this time attaching it near the other voltage maxima of
>the 3/4 wave mode - say about 1/3rd the way up the resonator.
>
>This 'middle' capacitance affects the 3/4 wave mode more than
>the 1/4 wave mode, so we now have the means of tuning each mode
>with some independence of the other. This tends to be done by
>splitting the coil at the appropriate point and maintaining the
>connection with a piece of wire (the 'transmission line' of
>magnifier terminology). The resonator now finds extra
>capacitive loading near its 3/4 wave voltage maxima: the top
>end-effect C of the secondary, plus the transmission line C,
>plus the lower end-effect C of the tertiary.
>
>If done correctly, the 3/4 wave mode is now timed to reach
>a voltage peak simultaneously with the fundamental after a
>certain (design choice) number of RF cycles have elapsed.
>
>Why bother going to all this trouble? Well the 3/4 wave
>mode is excited anyway, to some extent, whether we like it
>or not. So rather than waste that energy, we might as well
>try to use it. The extent to which higher modes are excited
>in any coil depends on how the primary induction is distributed
>along the coil. If we want to achieve high coupling (for what-
>ever reason) we cannot do so by spreading the primary along
>the secondary, for reasons of voltage breakdown. So we have
>to apply strong coupling to just a short region of the
>secondary at its cold end. It's this highly end-concentrated
>coupling which tends to put a greater proportion of the bang
>energy into the higher resonances of the secondary. Therefore
>it's a natural evolution of the TC to try to tame and exploit these.[*]
I do wonder how much useful extra energy is there and if we will waste energy
trying to get at the 3/4 wave's energy? Big magnifier's do well since they
are so big a two coil system just does not "fit". So breaking the coil up
into smaller parts has a big physical advantage.
>I've described all this to show how a bit of 'distributed'
>theory can be applied to understand the motivation for
>constructing magnifiers. (I must point out that when coilers
>think about magnifiers, they don't usually think about them in
>the kind of terms that I've used above). Antonio has
>thoroughly documented this tuning of multiple resonance networks using the lumped model,
>
>
http://www.coe.ufrj.br/~acmq/tesla/magnifier.html
>
>(There are of course 3 modes in operation in the magnifier,
>not just the two I mentioned above. The primary coil adds
>adds another relevant degree of freedom and when this is
>coupled to the secondary we find an additional 1/2 wave mode
>at work along the secondary-tertiary. This too is tuned to
>reach a top-volts peak simultaneously with the other two.) [+]
>
>You can see some modelled results for the mode spectrum of Thor, in the last
two graphs in
>
>
http://www.abelian.demon.co.uk/tssp/tmod.html
>
>This isn't a magnifier, just a heavily toploaded TC, but it
>shows the predicted levels and current distributions of eachof the resonances.
I think we need to consider streamer loading too. The lossless models are
neat, but streamer loading and losses changes things from the easy to calculate
world...
>Coiler's don't tend to take much notice of the higher order
>resonances of either primary or secondary. Many perhaps don't
>even realise they are there - mistaking the behaviour of the LC
>model for that of the real coil. Some coilers will admit that
>the secondary has lots of resonances, but will insist that
>the primary has only one, thinking perhaps that because it is
>more 'lumped' it is working in some basically different way.
>
>I should think most of the time this lack of awareness isn't
>any problem, after all the coils work. But I think it's
>useful to build up a mental picture of the distributed
>resonance, if only for the coiler's satisfaction of having a
>deeper understanding of the coil's behaviour.
>
>And there's always the hypothesis that some of this HF
>activity may contribute to the racing arc phenomena.
>If for example, one of the primary resonances happens to
>be similar in frequency to one of the secondary resonances.
>Say the first primary overtone collided with, say, the
>5th overtone of the secondary, there's nothing to prevent
>the two coils transferring energy back and forth at thesehigh frequencies.
The higher order stuff "may" dramatically affect spark gap quenching and
streamer propagation!!!
>Admittedly the various overtone amplitudes are small compared
>with fundamental. But set against this is the fact that
>the peak-trough distance of the overtone standing waves
>spans fewer turns along the coil than does the fundamental -
>fewer in inverse proportion to the number of quarter-waves.
>
>Plus they sit atop the pedestal of the large 1/4 wave voltage,
>so at the very least they will eat into the coil's breakdown 'headroom'.
>
>Racing arcs tend to be cured by small adjustments to topload
>height or coupling, eg raising the secondary or lowering the
>primary. When we model these kind of changes, we don't see
>any great change in the voltage gradients reached. Nor do
>models show any real gradient problems under out of tune
>conditions. One wonders then why the real coils seem to show
>such sensitivity to coupling and topload height with respect
>to racing arcs. One thing our models *dont* account for is
>the effect of primary overtones. It may be conceivable that
>the small adjustments mentioned are having the side effect
>of shifting the mode spectra of one or both coils with the
>unwitting consequence of removing a nasty collision of HF resonances.
Racing arcs and super powerful primary to secondary arcing just are not
well explained now.... I have watched primary to secondary arcs blow
through 1/4 inch G-10 I am just stunned that they can exist and do
that!!! The energy concentration in those arcs is doing something
"odd"!!! I have always turned to "transformer action", but the models
don't seem to support that well... Suppose 1 foot up the coil, there was
suddenly a 6 inch low R path to ground?.... Would the arc energy be "BIG"?
<Snip>
>Paul Nicholson
Cheers, Terry.
Date : Tue, 20 Jul 2004 08:12:20 -0600. Subject : Re: Resonance, and now magnifiers
Original
poster: "Dr. Resonance"
Perhaps I should say it another way: A large topload helps to reduce unwanted
small resonances at frequencies higher than the fundamental frequency. Even
though these resonances may be small they effectively "steal energy" that should
go towards the fundamental resonance point in the sec coil.
Also, all resonances, however small or large, can begin "beating" against each
other and form small standing waves which can interfere (destructive &
constructive interference) with the lower fundamental resonance. These unwanted
frequencies can produce unequal potentials across the sec coil, and specifically
in the case of small toploaded resonators, along with too much coupling, can
produce the dreaded "racing sparks". Dr. Resonance.
Date : Tue, 20 Jul 2004 08:14:17 -0600. Subject : Re: Resonance, and now magnifiers
Original
poster: Bert Pool
On my large magnifier, I use a 12 inch wide, fifteen foot long strip of aluminum
flashing as a transmission line. The surface area is quite large, because both
exposed sides provide capacitance, as opposed to a cylinder which has an inside
surface area that is wasted. The magnifier system loves the capacitance, and
Paul's explanation does a very good job of explaining why. The transmission
line, if designed as a large capacitance, acts as an additional energy storage
device, as well as bringing that 3/4 mode resonance more into "tune" with the
extra coil/topload.
Tesla ,himself, said adding capacitance to the top of the secondary of a
magnifier would improve operation (Colorado Springs Notes, September 19, 1899
page).
Date : Tue, 20 Jul 2004 21:05:44 -0600. Subject : Re: Resonance, and now magnifiers
Original
poster: humanb@chaoticuniverse.com
Yes, this is a vary interesting subject, thanks for the enlightening post Paul.
I have a quick question for Steve Conner, though: Steve has anyone yet figured
out how to "self-resonate" a ISSTC magnifier? I tried base current feed-back to
no avail. Definitely didn't pickup on the correct mode. In fact I couldn't get
it to oscillate at all. I may revisit this sometime later.
David Trimmell.
Date : Wed, 21 Jul 2004 07:18:21 -0600. Subject : Re: Resonance, and now magnifiers
Original
poster: "Dr. Resonance"
One could use flat copper strip, then slit some 1 inch dia. copper tubing, and
silver solder it over each end of the flat strip. Good field control at the
sharp edges. Dr. Resonance.
Date : Fri, 23 Jul 2004 11:58:14 -0600. Subject : Re: Resonance, and now magnifiers
Original
poster: "Paul Nicholson"
It might be worth listing again some of the other possible advantages of the
magnifier configuration. Items in this list don't depend on any of the
'exploitation of overtones' that we've been discussing, but stand on their own
as independent justifications. Some of these were mentioned recently in another
thread.
* It allows the hot end of the resonator to be located further away from the
primary stuff, eg several metres to one side.
* A large resonator may be more manageable in two pieces.
* Each coil can be replaced independently after damage, or redesigned, etc.
* Flexibility. The owner of N secondaries and M tertiaries has N*M possible
magnifiers in his possession. Or if you don't care which are secondary and
which are tertiary and just call them N assorted coils, you have N*(N-1)
magnifier combinations to play with.
Arguably then, there are some reasons for splitting up the resonator in this
way, whether or not there is any fancy tuning in mind.
Steve Conner wrote:
> If this is true, would a forced response magnifier that only
> excites the 1/4 wave mode be practical?
I'm sure it would be practical, and for the above reasons perhaps beneficial in
some cases. Indeed, doesn't the traditional CW coil, base fed via a ferrite
cored coupling transformer, fit this description? The initial normal mode
transient dies away as the
forced response builds up. To exploit higher overtones in this type of
operation, you would have to tune them to match a harmonic of the drive. Then a
square wave low Z (constant V) drive would cause current flow at the harmonic
frequency as well as the fundamental. Thus the overall input 'Z' would
seem lower and the coil would draw more total power from the driver. The
overtones would be tuned to the drive harmonics by hooking capacitance to the
coil in various places.
> Does a successful magnifier tuning manipulate the 3/4 wave
> mode to cause a voltage _minimum_ around the top of the
> driver coil and bottom of the extra coil?
The 3/4 wave mode would have its voltage maxima somewhere in the vicinity of the
junction of the two coils. But does it have to sit on the transmission
line? I'll try to discuss that.
If you just pick two coils at random and string them in series, there's only a
slim chance that the 3/4 wave maxima will be at the junction. Odds are more
likely it will reside inside one coil or the other. (Wherever it is, it'll move
upwards as tertiary top-C is applied.)
I'm pretty sure (but haven't actually checked) that as you go about loading the
transmission line with extra capacitance, the effect on the 3/4 wave voltage
distribution is to draw the maxima towards the junction from whichever coil it
started out in. That'll have to be checked to make sure.
Similar comments apply to the voltage node (minima) of the middle
resonance. Now I referred to this as a 1/2 wave in a previous post, but then I
remembered that Antonio had shown us it was really another 3/4 wave...
Antonio wrote (on 18th Nov 2003):
> The low-frequency component rises continuously along the coils (1/4 wave).
> The middle-frequency component is zero at the transmission
> line and accounts always for one half of the output voltage
> (3/4 wave with zero at the transmission line, or a degenerate
> 1/4 wave mode that starts at the transmission line).
> The high-frequency component is always negative at the
> transmission line, to cancel the first component there,
> and positive at the top. (3/4 wave too, with a zero
> somewhere at the third coil).
which sums things up very nicely. Since we appear to have two modes that look
like a 3/4 wave (one of which, the middle, would like to be 1/4 wave or maybe
1/2 wave but for its interaction with the primary), it might be better just to
number the modes, in order of frequency, as say
mode 1: secondary and tertiary combined is 1/4 wave;
mode 2: secondary is 1/2 wave, tertiary is 1/4 wave, total 3/4 wave;
mode 3: secondary is 1/4 wave, tertiary is 1/2 wave, total 3/4 wave;
A while ago I made up animations of these three modes for a hypothetical
magnifier, to illustrate what they look like.
http://hot-streamer.com/tssp/tmp/mag1.mode1.anim.gif
http://hot-streamer.com/tssp/tmp/mag1.mode2.anim.gif
http://hot-streamer.com/tssp/tmp/mag1.mode3.anim.gif
In these animations the secondary spans 0-30% of the graph, the tertiary 30% to
100%, so you can see the little discontinuity in the graphs at that
boundary. The modelled primary is a helical around the lower half of the
secondary (0 to 15%) so the pri-sec coupling is high.
These modelled coils where picked at random, and lo and behold we got the mode 3
maxima at 50%, ie 20% above the transmission line/junction. The mode 2 minima
is about 10% above the junction.
The combined motion of all three resonances looks like
http://hot-streamer.com/tssp/tmp/mag1.anim.gif
The tuning target is to get all three modes to coincide at a joint top volts
peak at the same instant. This in itself doesn't require the mode 3 voltage
maxima to be on the transmission line, nor the mode 2 voltage zero. But if we
also want to obtain the maximum energy transfer to the top end of the tertiary,
there is another condition to maintain...
Bert Pool has given an example of the large transmission line capacitance which
can be favourably used:-
> I use a 12 inch wide, fifteen foot long strip of
> aluminum flashing as a transmission line.
This can store a lot of energy per volt and we would like as an additional
requirement to arrange things so that at the instant the 3 modes meet their
simultaneous topvolts peak, the 3 modes also combine momentarily to give zero
volts at the transmission line.
This additional requirement ensures that all the energy is removed from that
intermediate storage and passed on. Ideally, mode 2 is identically zero because
we put its voltage node on the t-line. So we just need mode 1 and mode 3 to be
momentarily equal in
amplitude but opposite in polarity so they add to zero, also at the t-line.
(This certainly isn't happening in the modelled system above, which is just at a
random tuning. Nor is it likely to happen in a real magnifier, except either by
accident or by some very careful planning.)
Now I target the t-line for the scene of this momentary zeroing of stored energy
because this is likely where there greatest capacitance is located, and
therefore is the best place to remove all the energy from. But wherever we
choose to take advantage of this momentary zero, we'll still have non-zero volts
elsewhere in the coils and inevitably some energy must remain in the E-field of
the coils rather than the E-field of the top C.
Note that with this tuning, the entire peak topvolts is momentarily expressed
across the tertiary.
Suppose we now rope in further overtones. The effect is to introduce additional
points along the coils where the voltage can be made momentarily zero at the
appropriate instant. As we add more and more carefully timed overtones into the
mix, we see that we can achieve more and more cancellations coincident with the
joint topvolts peak.
In this way we tend towards a system portrayed by a single pulse travelling up
the coils, building in amplitude to wash against the topload leaving the coils
momentarily largely bereft of voltage.
Perhaps Antonio can confirm that description accords with his models of higher
order networks. The result I think tends towards a broadband pulse TC, perhaps
not dissimilar to pulse forming networks in radar magnetron supplies and that
sort of thing.
But unfortunately again, the entire topvolts is momentarily set across the
top-most coil, which must set a limit to how far we can go with cramming all the
stored E-field energy into the top end of the resonator in this manner.
It's a daunting prospect to face designing and tuning to this overtone
harnessing recipe. Perhaps only Antonio has ever managed to do that. Not only
do we have to tune the frequencies of the modes to achieve that joint topvolts
peak, we also have to tailor
their voltage distributions and relative amplitudes in order to achieve that
momentary zero on the t-line necessary for max energy transfer to the
topload. Quite a tall order.
More realistically, it might be better to ask what the proud owner of an
existing magnifier might do to check out and exploit some of these ideas. It
ought to be possible to examine an existing system that already works quite well
with a view to determining where the maxima and minima of each mode sit, and to
what extent the three modes are in the correct tuning for a joint topvolts
peak. On the basis of such an examination, it might to be possible to determine
some (perhaps small) adjustment which will in principle improve things. One
thing working for us is that we have software that can model all this for any
particular installation. Perhaps some of this will be a tempting line of
research for an advanced coiler. Paul Nicholson.
Date : Fri, 23 Jul 2004 12:05:28 -0600. Subject : Re: Resonance, and now magnifiers
Original
poster: "Paul Nicholson"
Ed Phillips wrote:
> I've always suspected the reason the top loading helps is that the
> greater amount of energy stored when the streamers start.
Yes. We often hear alternative suggestions involving choosing the topload to
achieve some kind of 'ideal' resonance condition within the resonator
itself. But as Ed, Terry, and others have said, the topload should be chosen
with a view to optimising the generation of streamers (at least for the intended
application of most TCs!) Quite how to do that is anybody's guess - the general
idea seems to be 'large is good'.
> As for the impedance of the discharges themselves, I suspect
> they're so low compared to the equivalent parallel losses of
> the secondary that the "unloaded Q" of any decent design really
> doesn't affect performance much.
Yes, the discharge loading will be high (assuming the topload is doing its job
properly) so would be seen as a low-ish impedance shunting the topload to
ground. Perhaps the Q of the resonator thus loaded would be down to 5 or 10 or
20, against an unloaded Q of say 50 at least. The efficiency of transfer of
energy from resonator to discharge is given by
Eff = 100% * (Qunloaded - Qloaded)/Qunloaded
That means if the topload is not working right, loaded Q will be higher than it
need be, and you'll be heating up the coil instead of the streamers.
Also, as Dr. Resonance wrote:
> A large topload helps to reduce unwanted small resonances at
> frequencies higher than the fundamental frequency.
Yes, perhaps in two distinct ways:
1) The large top-C pulls the 1/4 wave frequency way down from the overtones, so
perhaps reducing the proportion of energy going into them.
2) The large top-C brings down the top end impedance at the overtone
frequencies, ie reducing the voltages but the stored energy in the overtones
stays the same.
I still wonder about the 'unwanted' part though. Certainly as Dr. Resonance
goes on to say
> Also, all resonances, however small or large, can begin "beating"
> against each other and form small standing waves which can
> interfere (destructive & constructive interference) with the
> lower fundamental resonance.
We have lots of little standing waves and the beating between them appears as a
whole mess of little ripples and transients running up and down the coil. Their
amplitudes, though small, can be induced across small numbers of turns due to
the short wavelengths.
> These unwanted frequencies can produce unequal potentials
> across the sec coil
The effect is seen in this animation
http://www.abelian.demon.co.uk/tssp/cmod/jftt42a.grad.gif
showing the voltage gradients in one of John Freau's coils. At the the start of
the bang the initial excitation of overtones due to the end-concentrated primary
induction takes the form of a transient which rapidly traverses the coil and
reflects back and forth.
After a few lengths of the coil it has dispersed into a jangling mess of
incoherent overtone resonances. You can see in John's coil that this HF stuff
has quite a few kV/cm to contribute to the overall voltage gradient that the
turns have to withstand.
So yes, unwanted I think in this respect. But set against this is the
beneficial possibility that the HF currents may contribute to heating of the
breakout plasma. Even though the voltage amplitudes are relatively small at the
topload, the low impedance could drive
a substantial bunch of charge rapidly back and forth through the leaders with
each half cycle of the high frequency oscillations.
Perhaps then, a balanced diet of for feeding TC discharges is a mix of large low
frequency voltage to push out the streamers plus some high frequency stuff to
keep the leader channels hot. It might be possible to look for this
experimentally in a number of ways.
Well I'd better bring this thread on resonance to a close because I've said all
I can just about. If I seem to labour a few things it's because
a) It's
interesting, if nothing else.
b) There's a few misapprehensions in circulation which may appear fairly
innocent and perhaps subtle to many coilers, but which can result in some
individuals wasting a lot of time on futilities.
c) Someone was asking about ideas for experiments and research a while back. In
the last few years there's been a lot of talk and modelling and speculation
about the HF behaviour of TCs. But no one has really got to grips with the
experimental/practical side
of observing, testing, refuting, exploiting, etc.
A summary of some specific open practical questions:-
1) Do HF overtones have any bearing on racing arcs?
2) Is there any beneficial discharge heating effect from HF currents?
3) Can magnifier overtones be tuned into contributing to output voltage and
efficiency?
4) Can overtones be tuned to match drive harmonics in the CW TC, and is there
anything to gain?
We just don't even know whether any of this overtone stuff matters at all. If
some reliable experimenter could just answer that question, at least we'd know
whether to stop thinking about it and do something else instead. Paul
Nicholson, Manchester, UK.
Date : Sat, 24 Jul 2004 11:33:46 -0600. Subject : Re: Resonance, and now magnifiers
Original
poster: "Paul Nicholson"
It might be worth listing again some of the other possible advantages of the
magnifier configuration. Items in this list don't depend on any of the
'exploitation of overtones' that we've been discussing, but stand on their own
as independent justifications. Some of these were mentioned recently in another
thread.
* It allows the hot end of the resonator to be located further away from the
primary stuff, e. g., several metres to one side.
* A large resonator may be more manageable in two pieces.
* Each coil can be replaced independently after damage, or redesigned, etc.
* Flexibility. The owner of N secondaries and M tertiaries has N*M possible
magnifiers in his possession. Or if you don't care which are secondary and
which are tertiary and just call them N assorted coils, you have N*(N-1)
magnifier combinations to play with.
Arguably then, there are some reasons for splitting up the resonator in this
way, whether or not there is any fancy tuning in mind.
Steve Conner wrote:
> If this is true, would a forced response magnifier that only
> excites the 1/4 wave mode be practical?
I'm sure it would be practical, and for the above reasons perhaps beneficial in
some cases. Indeed, doesn't the traditional CW coil, base fed via a ferrite
cored coupling transformer, fit this description? The initial normal mode
transient dies away as the
forced response builds up. To exploit higher overtones in this type of
operation, you would have to tune them to match a harmonic of the drive. Then a
square wave low Z (constant V) drive would cause current flow at the harmonic
frequency as well as the fundamental. Thus the overall input 'Z' would seem
lower and the coil would draw more total power from the driver. The overtones
would be tuned to the drive harmonics by hooking capacitance to the coil in
various places.
> Does a successful magnifier tuning manipulate the 3/4 wave mode to cause a voltage
>_minimum_ around the top of the driver coil and bottom of the extra coil?
The 3/4 wave mode would have its voltage maxima somewhere in the vicinity of the
junction of the two coils. But does it have to sit on the transmission
line? I'll try to discuss that.
If you just pick two coils at random and string them in series, there's only a
slim chance that the 3/4 wave maxima will be at the junction. Odds are more
likely it will reside inside one coil or the other. (Wherever it is, it'll move
upwards as tertiary top-C is applied.)
I'm pretty sure (but haven't actually checked) that as you go about loading the
transmission line with extra capacitance, the effect on the 3/4 wave voltage
distribution is to draw the maxima towards the junction from whichever coil it
started out in. That'll have to be checked to make sure.
Similar comments apply to the voltage node (minima) of the middle
resonance. Now I referred to this as a 1/2 wave in a previous post, but then I
remembered that Antonio had shown us it was really another 3/4 wave...
Antonio wrote (on 18th Nov 2003):
> The low-frequency component rises continuously along the coils (1/4 wave).
> The middle-frequency component is zero at the transmission
> line and accounts always for one half of the output voltage
> (3/4 wave with zero at the transmission line, or a degenerate
> 1/4 wave mode that starts at the transmission line).
> The high-frequency component is always negative at the
> transmission line, to cancel the first component there,
> and positive at the top. (3/4 wave too, with a zero
> somewhere at the third coil).
which sums things up very nicely. Since we appear to have two modes that look
like a 3/4 wave (one of which, the middle, would like to be 1/4 wave or maybe
1/2 wave but for its interaction with the primary), it might be better just to
number the modes, in order of frequency, as say
mode 1: secondary and tertiary combined is 1/4 wave;
mode 2: secondary is 1/2 wave, tertiary is 1/4 wave, total 3/4 wave;
mode 3: secondary is 1/4 wave, tertiary is 1/2 wave, total 3/4 wave;
A while ago I made up animations of these three modes for a hypothetical
magnifier, to illustrate what they look like.
http://hot-streamer.com/tssp/tmp/mag1.mode1.anim.gif
http://hot-streamer.com/tssp/tmp/mag1.mode2.anim.gif
http://hot-streamer.com/tssp/tmp/mag1.mode3.anim.gif
In these animations the secondary spans 0-30% of the graph, the tertiary 30% to
100%, so you can see the little discontinuity in the graphs at that
boundary. The modelled primary is a helical around the lower half of the
secondary (0 to 15%) so the pri-sec coupling is high.
These modelled coils where picked at random, and lo and behold we got the mode 3
maxima at 50%, ie 20% above the transmission line/junction. The mode 2 minima
is about 10% above the junction.
The combined motion of all three resonances looks like
http://hot-streamer.com/tssp/tmp/mag1.anim.gif
The tuning target is to get all three modes to coincide at a joint top volts
peak at the same instant. This in itself doesn't require the mode 3 voltage
maxima to be on the transmission line, nor the mode 2 voltage zero. But if we
also want to obtain the maximum energy transfer to the top end of the tertiary,
there is another condition to maintain...
Bert Pool has given an example of the large transmission line capacitance which
can be favourably used:-
> I use a 12 inch wide, fifteen foot long strip of
> aluminum flashing as a transmission line.
This can store a lot of energy per volt and we would like as an additional
requirement to arrange things so that at the instant the 3 modes meet their
simultaneous topvolts peak, the 3 modes also combine momentarily to give zero
volts at the transmission line.
This additional requirement ensures that all the energy is removed from that
intermediate storage and passed on. Ideally, mode 2 is identically zero because
we put its voltage node on the t-line. So we just need mode 1 and mode 3 to be
momentarily equal in
amplitude but opposite in polarity so they add to zero, also at the t-line.
(This certainly isn't happening in the modelled system above, which is just at a
random tuning. Nor is it likely to happen in a real magnifier, except either by
accident or by some very careful planning.)
Now I target the t-line for the scene of this momentary zeroing of stored energy
because this is likely where there greatest capacitance is located, and
therefore is the best place to remove all the energy from. But wherever we
choose to take advantage of this momentary zero, we'll still have non-zero volts
elsewhere in the coils and enivitably some energy must remain in the E-field of
the coils rather than the E-field of the top C.
Note that with this tuning, the entire peak topvolts is momentarily expressed
across the tertiary.
Suppose we now rope in further overtones. The effect is to introduce additional
points along the coils where the voltage can be made momentarily zero at the
appropriate instant. As we add more and more carefully timed overtones into the
mix, we see that we can achieve more and more cancellations coincident with the
joint topvolts peak.
In this way we tend towards a system portrayed by a single pulse travelling up
the coils, building in amplitude to wash against the topload leaving the coils
momentarily largely bereft of voltage.
Perhaps Antonio can confirm that description accords with his models of higher
order networks. The result I think tends towards a broadband pulse TC, perhaps
not dissimilar to pulse forming networks in radar magnetron supplies and that
sort of thing.
But unfortunately again, the entire topvolts is momentarily set across the
top-most coil, which must set a limit to how far we can go with cramming all the
stored E-field energy into the top end of the resonator in this manner.
It's a daunting prospect to face designing and tuning to this overtone
harnessing recipe. Perhaps only Antonio has ever managed to do that. Not only
do we have to tune the frequencies of the modes to achieve that joint topvolts
peak, we also have to tailor
their voltage distributions and relative amplitudes in order to achieve that
momentary zero on the t-line necessary for max energy transfer to the
topload. Quite a tall order.
More realistically, it might be better to ask what the proud owner of an
existing magnifier might do to check out and exploit some of these ideas. It
ought to be possible to examine an existing system that already works quite well
with a view to determining where the maxima and minima of each mode sit, and to
what extent the three modes are in the correct tuning for a joint topvolts
peak. On the basis of such an examination, it might to be possible to determine
some (perhaps small) adjustment which will in principle improve things. One
thing working for us is that we have software that can model all this for any
particular installation. Perhaps some of this will be a tempting line of
research for an advanced coiler. Paul Nicholson.
Date : Sat, 24 Jul 2004 11:34:19 -0600. Subject : Re: Resonance, and now magnifiers
Original
poster: "Paul Nicholson"
Ed Phillips wrote:
> I've always suspected the reason the top loading helps is that the
> greater amount of energy stored when the streamers start.
Yes. We often hear alternative suggestions involving choosing the topload to
achieve some kind of 'ideal' resonance condition within the resonator
itself. But as Ed, Terry, and others have said, the topload should be chosen
with a view to optimising the generation of streamers (at least for the intended
application of most TCs!) Quite how to do that is anybody's guess - the general
idea seems to be 'large is good'.
> As for the impedance of the discharges themselves, I suspect
> they're so low compared to the equivalent parallel losses of
> the secondary that the "unloaded Q" of any decent design really
> doesn't affect performance much.
Yes, the discharge loading will be high (assuming the topload is doing its job
properly) so would be seen as a low-ish impedance shunting the topload to
ground. Perhaps the Q of the resonator thus loaded would be down to 5 or 10 or
20, against an unloaded Q of say 50 at least. The efficiency of transfer of
energy from resonator to discharge is given by
Eff = 100% * (Qunloaded - Qloaded)/Qunloaded
That means if the topload is not working right, loaded Q will be higher than it
need be, and you'll be heating up the coil instead of the streamers.
Also, as Dr. Resonance wrote:
> A large topload helps to reduce unwanted small resonances at
> frequencies higher than the fundamental frequency.
Yes, perhaps in two distinct ways:
1) The large top-C pulls the 1/4 wave frequency way down from the overtones, so
perhaps reducing the proportion of energy going into them.
2) The large top-C brings down the top end impedance at the overtone
frequencies, ie reducing the voltages but the stored energy in the overtones
stays the same.
I still wonder about the 'unwanted' part though. Certainly as Dr. Resonance
goes on to say
> Also, all resonances, however small or large, can begin "beating"
> against each other and form small standing waves which can
> interfere (destructive & constructive interference) with the lower fundamental resonance.
We have lots of little standing waves and the beating between them appears as a
whole mess of little ripples and transients running up and down the coil. Their
amplitudes, though small, can be induced across small numbers of turns due to
the short wavelengths.
> These unwanted frequencies can produce unequal potentials across the sec coil
The effect is seen in this animation
http://www.abelian.demon.co.uk/tssp/cmod/jftt42a.grad.gif
showing the voltage gradients in one of John Freau's coils. At the the start of
the bang the initial excitation of overtones due to the end-concentrated primary
induction takes the form of a transient which rapidly traverses the coil and
reflects back and forth.
After a few lengths of the coil it has dispersed into a jangling mess of
incoherent overtone resonances. You can see in John's coil that this HF stuff
has quite a few kV/cm to contribute to the overall voltage gradient that the
turns have to withstand.
So yes, unwanted I think in this respect. But set against this is the
beneficial possibility that the HF currents may contribute to heating of the
breakout plasma. Even though the voltage amplitudes are relatively small at the
topload, the low impedance could drive
a substantial bunch of charge rapidly back and forth through the leaders with
each half cycle of the high frequency oscillations.
Perhaps then, a balanced diet of for feeding TC discharges is a mix of large low
frequency voltage to push out the streamers plus some high frequency stuff to
keep the leader channels hot. It might be possible to look for this
experimentally in a number of ways.
Well I'd better bring this thread on resonance to a close because I've said all
I can just about. If I seem to labour a few things it's because
a) It's interesting, if nothing else.
b) There's a few misapprehensions in circulation which may appear fairly
innocent and perhaps subtle to many coilers, but which can result in some
individuals wasting a lot of time on futilities.
c) Someone was asking about ideas for experiments and research a while back. In
the last few years there's been a lot of talk and modelling and speculation
about the HF behaviour of TCs. But no one has really got to grips with the
experimental/practical side
of observing, testing, refuting, exploiting, etc.
A summary of some specific open practical questions:-
1) Do HF overtones have any bearing on racing arcs?
2) Is there any beneficial discharge heating effect from HF currents?
3) Can magnifier overtones be tuned into contributing to output voltage and
efficiency?
4) Can overtones be tuned to match drive harmonics in the CW TC, and is there
anything to gain?
We just don't even know whether any of this overtone stuff matters at all. If
some reliable experimenter could just answer that question, at least we'd know
whether to stop thinking about it and do something else instead. Paul
Nicholson, Manchester, UK.
